Non-quasiconvex subgroups of hyperbolic groups via Stallings-like techniques

Pallavi Dani; Ivan Levcovitz

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arXiv · 2102.11853

Non-quasiconvex subgroups of hyperbolic groups via Stallings-like techniques

Pallavi Dani·Ivan Levcovitz

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Abstract

We provide a new method of constructing non-quasiconvex subgroups of hyperbolic groups by utilizing techniques inspired by Stallings' foldings. The hyperbolic groups constructed are in the natural class of right-angled Coxeter groups (RACGs for short) and can be chosen to be 2-dimensional. More specifically, given a non-quasiconvex subgroup of a (possibly non-hyperbolic) RACG, our construction gives a corresponding non-quasiconvex subgroup of a hyperbolic RACG. We use this to construct explicit examples of non-quasiconvex subgroups of hyperbolic RACGs including subgroups whose generators are as short as possible (length two words), finitely generated free subgroups, non-finitely presentable subgroups, and subgroups of fundamental groups of square complexes of nonpositive sectional curvature.

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Pallavi Dani, Ivan Levcovitz. 2021-02-23. Non-quasiconvex subgroups of hyperbolic groups via Stallings-like techniques. https://arxiv.org/abs/2102.11853

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